Centre of Mass Class 11 - IIT JEE | NEET

The centre of mass is the single point in a body or system of bodies that moves as if all the mass were concentrated there and all external forces were applied at that point. For a uniform object, it lies at the geometric centre. For a non-uniform object, it shifts toward the heavier side.

For two particles of mass m₁ and m₂ at positions x₁ and x₂ on the x-axis, the centre of mass is at x_cm = (m₁x₁ + m₂x₂) / (m₁ + m₂). The point always lies between the two masses and is closer to the heavier mass.

No. The centre of mass can lie outside the physical boundary of the body. A classic example is a uniform ring — its centre of mass is at the geometric centre, which is in empty space at the middle of the ring. Similarly, for a horseshoe-shaped object, the COM lies in the air between the two arms.

Yes. Centre of mass and linear momentum conservation appear in almost every NEET paper, contributing 1–2 questions. The sub-topics most tested in NEET are the COM formula for discrete systems, momentum conservation during collisions, and perfectly inelastic collision results. These are straightforward once the formulas are clearly understood.

The total linear momentum of a system equals the total mass multiplied by the velocity of the centre of mass: P = Mv_cm. When no net external force acts, v_cm is constant — meaning the centre of mass moves in a straight line at constant speed, even if individual particles are colliding or exploding internally.